From small-angle neutron scattering studies of the flux line lattice (FLL) in CeCoIn5, with magnetic field applied parallel to the crystal c-axis, we obtain the field and temperature dependence of the FLL form factor (FF), which is a measure of the spatial variation of the field in the mixed state. We extend our earlier work (Bianchi et al 2008 Science 319 177) to temperatures up to 1250 mK. Over the entire temperature range, paramagnetism in the flux line cores results in an increase of the FF with field. Near H-c2 the FF decreases again, and our results indicate that this fall-off extends outside the proposed Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) region. Instead, we attribute the decrease to a paramagnetic suppression of Cooper pairing. At higher temperatures, a gradual crossover toward more conventional mixed state behavior is observed.